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The Steepest Descent Method for Forward-Backward SDEs

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	The Steepest Descent Method for Forward-Backward SDEs
2.	Creator	Author's name, affiliation, country	Jaksa Cvitanic; California Institute of Technology, USA
2.	Creator	Author's name, affiliation, country	Jianfeng Zhang; University of Southern California, USA
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)
4.	Description	Abstract	This paper aims to open a door to Monte-Carlo methods for numerically solving Forward-Backward SDEs, without computing over all Cartesian grids as usually done in the literature. We transform the FBSDE to a control problem and propose the steepest descent method to solve the latter one. We show that the original (coupled) FBSDE can be approximated by {it decoupled} FBSDEs, which further comes down to computing a sequence of conditional expectations. The rate of convergence is obtained, and the key to its proof is a new well-posedness result for FBSDEs. However, the approximating decoupled FBSDEs are non-Markovian. Some Markovian type of modification is needed in order to make the algorithm efficiently implementable.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2005-12-19
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/295
10.	Identifier	Digital Object Identifier	10.1214/EJP.v10-295
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 10
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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